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It is shown that among all connected cographs of order $n \\ge 7$, the star $K_{1,n-1}$ has maximum mean connected induced subgraph order, and for $n \\ge 3$, the $n$-skillet, $K_1+(K_1 \\cup K_{n-2})$, has minimum mean connected induced subgraph order. It is deduced that the density for connected cographs (i.e. the ratio of the mean to the order of the graph) is asymptotically $1/2$. The mean order of all connected induced subgraphs containing a given vertex $v$ of a cograph $G$,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.01916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-06T17:39:24Z","cross_cats_sorted":[],"title_canon_sha256":"5a97ad0fe14d01be5eb1eb81193a157141ffda865e44464fba54ce4e5f8dda80","abstract_canon_sha256":"62bf6f152b2d8a3dca83765c6e52eb7c64449427b34d7982e684960f8fdc21a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:32.781567Z","signature_b64":"9J66FURmfDTx+1u1BNDTUU10WPXzZ6JzW3N0gYHdZIc8YWQWjPjpYFUW3zsT947zKNamYUsvRCkP9LFilaZDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74bf137ccff91ffa736af28b04e3a91cec6d48177523ae108dc56d254255506e","last_reissued_at":"2026-05-18T00:38:32.781126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:32.781126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Mean Connected Induced Subgraph Order of Cographs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucas Mol, Matthew E. Kroeker, Ortrud R. Oellermann","submitted_at":"2017-08-06T17:39:24Z","abstract_excerpt":"In this article the extremal structures for the mean order of connected induced subgraphs of cographs are determined. It is shown that among all connected cographs of order $n \\ge 7$, the star $K_{1,n-1}$ has maximum mean connected induced subgraph order, and for $n \\ge 3$, the $n$-skillet, $K_1+(K_1 \\cup K_{n-2})$, has minimum mean connected induced subgraph order. It is deduced that the density for connected cographs (i.e. the ratio of the mean to the order of the graph) is asymptotically $1/2$. 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